Automatic Differentiable Monte Carlo: Theory and Application
This work addresses a key bottleneck for researchers in statistics and physics by enabling the integration of modern machine learning frameworks with traditional Monte Carlo simulations, though it appears incremental as it builds on existing differentiable programming paradigms.
The paper tackles the challenge of applying differentiable programming to Monte Carlo methods, presenting a general theory for infinite-order automatic differentiation on expectations with unnormalized distributions, called automatic differentiable Monte Carlo (ADMC). It demonstrates applications such as fast phase transition search and accurate ground state finding in 2D many-body models, showing potential for higher accuracy and efficiency in areas like solving the sign problem in quantum models.
Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the general theory enabling infinite-order automatic differentiation on expectations computed by Monte Carlo with unnormalized probability distributions, which we call "automatic differentiable Monte Carlo" (ADMC). By implementing ADMC algorithms on computational graphs, one can also leverage state-of-the-art machine learning frameworks and techniques to traditional Monte Carlo applications in statistics and physics. We illustrate the versatility of ADMC by showing some applications: fast search of phase transitions and accurately finding ground states of interacting many-body models in two dimensions. ADMC paves a promising way to innovate Monte Carlo in various aspects to achieve higher accuracy and efficiency, e.g. easing or solving the sign problem of quantum many-body models through ADMC.